就那个常用卷积

$id_k * 1 = \sigma_k$

$\mu * id = \phi$

$\phi * 1 = id$

$\mu * 1 = \epsilon$

$\sigma_0 * \mu = 1$

就那个狄利克雷前/后缀和

$O(nlog(logn))$

$g(d)=\sum \limits _{d|T}f(T)$

for (int i = 0; i < cnt; i++) {
    for (int j = n / primes[i]; j; j--) {
        f[j] += f[j * primes[i]];
    }
}

$g(T)=\sum \limits _{d|T}f(d)$

for (int i = 0; i < cnt; i++) {
    for (int j = 1; j * primes[i] <= n; j++) {
        f[primes[i] * j] += f[j];
    }
}

就那个伯努利数和自然数幂和多项式的系数

$O(n^2)$

void init_B(int n) {
    B[0] = 1;
    for (int i = 1; i <= n; i++) {
        int sum = 0;
        for (int j = 0; j < i; j++) {
            sum = (sum + 1ll * c(i + 1, j) * B[j] % mod) % mod;
        }
        B[i] = (mod - 1ll * sum * qpow(c(i + 1, i), mod - 2) % mod);
    }
    for (int i = 0; i <= n; i++) {
        f[n + 1 - i] = 1ll * c(n + 1, i) * B[i] % mod * qpow(n + 1, mod - 2) % mod;
    }
}